Problem: $\lim_{x\to \frac{\pi}{4}}\cot(x)=?$ Choose 1 answer: Choose 1 answer: (Choice A) A $\dfrac{\sqrt{2}}{2}$ (Choice B) B $1$ (Choice C) C $\sqrt{2}$ (Choice D) D The limit doesn't exist.
$\cot(x)$ is continuous on all points in its domain. Therefore, if $x=\dfrac{\pi}{4}$ is within the domain of $\cot(x)$, we can find $\lim_{x\to \frac{\pi}{4}}\cot(x)$ by direct substitution. $x=\dfrac{\pi}{4}$ is indeed in the domain of $\cot(x)$ : $\begin{aligned} \cot\left(\dfrac{\pi}{4}\right)&=\dfrac{\cos\left(\dfrac{\pi}{4}\right)}{\sin\left(\dfrac{\pi}{4}\right)} \\\\ &=\dfrac{\left( \dfrac{\sqrt{2}}{2}\right)}{\left( \dfrac{\sqrt{2}}{2}\right)} \\\\ &=1 \end{aligned}$ $\lim_{x\to \frac{\pi}{4}}\cot(x)=1$